1. Field of Invention
The present invention relates generally to photonic radio frequency (RF) phase shifter and, more specifically, to photonic RF phase shifter with mitigated RF power fluctuation and devices incorporating the same.
2. Description of the Related Art
The implementation of phased array systems for radar and communication applications is hindered by the need for complex RF feed structures. See, J. Cowards, T. Yee, C. Chalfant, and P. Chang, “A Photonic Integrated-Optic RF Phase Shifter for Phased Array Antenna Beam-forming Applications,” IEEE J. of Lightwave Technology, vol. 11, no. 12, 1993, pp. 2201-5, incorporated herein by reference. Photonic approaches to beam forming have been identified as possible replacements for conventional complex and costly RF corporate feeds. Photonic RF phase shifters are important components of such photonic microwave signal-processing approaches. For example, a prior photonic RF phase shifter architecture initially proposed by Soref and demonstrated by Kamiya et al. and Lee et al. is flexible and easily implementable in that it does not require multiple detection elements, incoherent light sources, etc. See: R. Soref, “Voltage-Controlled Optical/RF Phase Shifter,” J. of Lightwave technology, vol. 3, no. 5, 1985, pp. 992-8; S. Lee, A. Udupa, H. Erlig, H. Zhang, Y. Chang, C. Zhang, D. Chang, D. Bhattacharya, B. Tsap, W. Steier, L. Dalton, and H. Fetterman, “Demonstration of a Photonically Controlled RF Phase Shifter,” IEEE Microwave and Guided Wave Lett., vol. 9, no. 9, 1999, pp. 357-9; and S. Lee, A. Udupa, H. Erlig, H. Zhang, Y. Chang, C. Zhang, D. Chang, D. Bhattacharya, B. Tsap, W. Steier, L. Dalton, and H. Fetterman, “Demonstration of a Photonically Controlled RF Phase Shifter,” IEEE Microwave and Guided Wave Lett., vol. 9, no. 9, 1999, pp. 357-9, all of which are incorporated herein by reference. However, this RF phase shifter structure suffers from the deficiency of experiencing large RF power fluctuations as the RF phase is tuned. Moreover, the RF phase of this structure changes non-linearly with control phase/bias.
Referring to FIG. 1, the photonic RF phase shifter structure 100 demonstrated by Kamiya et al. and Lee et al. includes a frequency shifter 102 and a phase controller 104 realized in the form of two nested Mach-Zehnder modulators configured as shown. The electrodes of the upper and lower arms of the frequency shifter 102 are respectively driven with the in-phase and quadrature components derived from the same microwave source. This inner modulator acts as a single side band (SSB) modulator, with the optical frequency increasing by the amount of RF frequency ω, and is embedded within the second Mach-Zehnder modulator. The optical phase in the other arm of the outer Mach-Zehnder is modulated by the quasi-DC electrical signal Vs, which controls the final RF phase of the microwave field. After the two outer arms are combined, there are two different optical frequencies or wavelengths existing in the output EO. When delivered to a photodetector, these two optical wavelengths provide a phase shifted RF signal through difference frequency generation. The RF signal encoded onto the optical carrier is recovered by demodulation performed with the photodetector.
The output intensity at the modulation frequency, which is responsible for the RF power generation in the photodetector, is given by                                                                         I                                  ω                  ,                  o                                            ∝                            ⁢                                                                    E                    i                    2                                    16                                ·                                  {                                                                                    [                                                                                                            2                                                        ⁢                                                                                          J                                1                                                            ⁡                                                              (                                                                                                      2                                                                    ⁢                                  Δ                                                                )                                                                                                              +                                                      4                            ⁢                                                                                          J                                1                                                            ⁡                                                              (                                Δ                                )                                                                                      ⁢                            sin                            ⁢                                                                                                                   ⁢                            φ                                                                          ]                                            ⁢                      sin                      ⁢                                                                                           ⁢                      ω                      ⁢                                                                                           ⁢                      t                                        -                                                                                                                                                           ⁢                                                                    [                                                                                            2                                                ⁢                                                                              J                            1                                                    ⁡                                                      (                                                                                          2                                                            ⁢                              Δ                                                        )                                                                                              +                                              4                        ⁢                                                                                                   ⁢                                                                              J                            1                                                    ⁡                                                      (                            Δ                            )                                                                          ⁢                        cos                        ⁢                                                                                                   ⁢                        φ                                                              ]                                    ⁢                  cos                  ⁢                                                                           ⁢                  ω                  ⁢                                                                           ⁢                  t                                }                                                                                        =                            ⁢                                                                    E                    i                    2                                    16                                ⁢                                  A                  ⁡                                      (                                          Δ                      ,                      φ                                        )                                                  ⁢                                  cos                  ⁡                                      (                                                                  ω                        ⁢                                                                                                   ⁢                        t                                            +                                              ϕ                        ⁡                                                  (                                                      Δ                            ,                            φ                                                    )                                                                                      )                                                                                                          (        1        )            where ω is the RF modulation frequency, Δ is the RF modulation depth, φ is the optical phase produced by the control signal Vs, the RF photocurrent is proportional to A (Δ, φ), and φ(Δ, φ) is the RF phase of the detected signal. Where Δ and φ are related to the electrical signals by                     Δ        =                  π          ⁢                                    V              m                                      V                              π                ,                RF                                                                        (2a)                                φ        =                  π          ⁢                                    V              s                                      V                              π                ,                                  D                  ⁢                                                                           ⁢                  C                                                                                        (2b)            where Vπ,RF and Vπ,DC are the RF and DC half-wave voltage, respectively. From (1), A and φ are related to Δ and φ as follows                               A          ⁡                      (                          Δ              ,              φ                        )                          =                                                            (                                                                            2                                        ⁢                                                                  J                        1                                            ⁡                                              (                                                                              2                                                    ⁢                          Δ                                                )                                                                              +                                      4                    ⁢                                                                                   ⁢                                                                  J                        1                                            ⁡                                              (                        Δ                        )                                                              ⁢                    sin                    ⁢                                                                                   ⁢                    φ                                                  )                            2                        +                                          (                                                                            2                                        ⁢                                                                  J                        1                                            ⁡                                              (                                                                              2                                                    ⁢                          Δ                                                )                                                                              +                                      4                    ⁢                                                                                   ⁢                                                                  J                        1                                            ⁡                                              (                        Δ                        )                                                              ⁢                    cos                    ⁢                                                                                   ⁢                    φ                                                  )                            2                                                          (3a)                                          tan          ⁢                                           ⁢                      ϕ            ⁡                          (                              Δ                ,                φ                            )                                      =                                                            2                            ⁢                                                J                  1                                ⁡                                  (                                                            2                                        ⁢                    Δ                                    )                                                      +                          4              ⁢                                                J                  1                                ⁡                                  (                  Δ                  )                                            ⁢              sin              ⁢                                                           ⁢              φ                                                                          2                            ⁢                                                J                  1                                ⁡                                  (                                                            2                                        ⁢                    Δ                                    )                                                      +                          4              ⁢                                                           ⁢                                                J                  1                                ⁡                                  (                  Δ                  )                                            ⁢              cos              ⁢                                                           ⁢              φ                                                          (3b)            From (3b), it can be seen that the microwave phase can be controlled by changes in φ (control phase) or changes in the control bias, Vs. FIG. 2 shows calculation results based on (3b) for three different values of RF modulation depth, Δ. For Δ equal to 2.7, the RF phase is linearly dependent on the control phase; however, to achieve this condition requires a considerable amount of RF drive power, Vm=(2.7/π)Vπ,RF. Moreover, at this drive level signal distortions are likely from the generation of first and second harmonics.
As disclosed in Lee et al., in order to avoid the generation of harmonics and signal distortion, Δ is set to ≦1, small signal operation. As Δ is reduced below 2.7, the linear dependence of the microwave phase on control phase disappears and it is replaced by a strong non-linear dependence.
Under small signal operation, in addition to the non-linear dependence of microwave phase on control phase, the generated RF power varies with microwave phase. See, D. Jez, K. Cearns, and P. Jessop, “Optical Waveguide Components For Beam Forming in Phased-Array Antennas,” Microwave and Optical Technology Letters, vol. 15, no. 1, 1997, pp. 46-49, incorporated herein by reference. The generated microwave power is given by                               P          g                =                              1            2                    ⁢                      R            d                    ⁢                                    {                                                RP                  o                                ⁢                                  A                  ⁡                                      (                                          Δ                      ,                      φ                                        )                                                              }                        2                                              (        4        )            where Pg is the generated microwave power at ω, Rd is the detector impedance, R is the detector responsivity, and Po is the product of the input optical power and the optical insertion loss. FIG. 3 shows calculations based on (4) for the case of Δ equal to 1. In the power calculation, the following parameters were assumed: Rd=50Ω, R==1 A/W, and Po=1 mW. As seen from the figure, the generated microwave power varies by up to 12 dB as the microwave phase varies over 2π. This is highly undesirable for the photonic control of phased arrays.
Mathematically, this detrimental effect arises from the terms containing J1(√{square root over (2)}Δ) in (3a). Physically, these terms arise from mixing of the optical frequency shifter arms. Under appropriate operating conditions, the optical frequency shifter is also a single side band modulator. See, M. Izutsu, S. Shikama, and T. Sueta, “Integrated Optical SSB Modulator/Frequency Shifter,” IEEE Journal of Quantum Elect., vol. QE-17, no. 11, 1981, pp. 2225-2227, which is incorporated herein by reference. The RF phase shifter structure of FIG. 1 cannot compensate for this effect and results in degraded shifter performance. Accordingly, it would be helpful in a photonic RF phase shifter structure (for photonic control of phase array systems among other things) to be able to reduce the microwave power variation as the microwave phase is tuned.